A doped iron-based superconductor Li$_x$(C$_5$H$_5$N)$_y$Fe$_2$Se$_2$ with $x \sim 0.6$ and $y \sim 0.7-0.9$ is investigated using nuclear magnetic resonance (NMR). Measurements of the spin-lattice relaxation time $T_1$ on selenium nuclei, which are key to superconductivity as a part of the FeSe planes, reveal unconventional superconductivity below the critical temperature $T_c = 39\,\mathrm{K}$. Temperature dependence of $T_1$ in the superconducting state is consistent with the so-called $s^\pm$ symmetry of the superconducting gap.
In the normal state, the selenium $T_1$ and the frequency shift of its NMR spectrum follow an unusually strong temperature dependence, which is described using a multiband model with one of the valence bands having its upper edge at $\tilde{\Delta} = 58\,\mathrm{meV}$ below the Fermi energy.
Measurements of lithium NMR spectra show that lithium plays a passive role in determining electronic characteristics in the normal and the superconducting state. It is important solely from the perspective of doping and structural stability of the material. Extremely slow relaxation of lithium nuclei suggests completely decoupled FeSe planes and two-dimensional physics within them.
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